AREA OF MUTUAL INTEREST AGREEMENT

Exhibit 10.4

Execution Version

AREA OF MUTUAL INTEREST AGREEMENT

     THIS AREA OF MUTUAL INTEREST AGREEMENT, dated as of March 17, 2009 (this “Agreement”), is entered into by and among Regency Energy Partners LP, a Delaware limited partnership (the “MLP”), RIGS Haynesville Partnership Co., a Delaware general partnership (the “Company”), Regency Haynesville Intrastate Gas LLC, a Delaware limited liability company (“Regency HIG”), Alinda Gas Pipeline I, L.P., a Delaware limited partnership (“Alinda Investor 1”) and Alinda Gas Pipeline II, L.P., a Delaware limited partnership (“Alinda Investor 2,” and collectively with Alinda Investor 1, the “Alinda Investors”). The parties to this Agreement are collectively referred to as the “Parties” and individually as a “Party.” Capitalized terms used but not defined herein have the meanings ascribed to them in that certain Contribution Agreement, dated as of February 26, 2009, by and among Regency HIG, the Company, General Electric Capital Corporation, a Delaware corporation, Alinda Investor 1 and Alinda Investor 2 (the “Contribution Agreement”).

RECITALS:

     WHEREAS, upon the Closing, (a) Regency HIG, an indirect wholly owned subsidiary of the MLP, will contribute a 99.999% limited partnership interest in Regency Intrastate Gas LP (“RIGS”) to the Company, (b) RIGS SPE LLC, an indirect wholly owned subsidiary of the MLP, will contribute a 0.001% general partnership interest in RIGS to RIGS GP LLC, a wholly owned subsidiary of the Company, and (c) the Company will issue the GP Units and pay the Regency Closing Payment to Regency HIG, in each case as described in the Contribution Agreement; and

     WHEREAS, pursuant to the Contribution Agreement, this Agreement is to be executed and delivered at Closing.

     NOW, THEREFORE, in consideration of their mutual undertakings and agreements hereunder, the Parties undertake and agree as follows:

     Section 1. Creation of AMI Opportunity.

     (a) Certain Definitions.

          “AMI Acquisition” means the acquisition of any AMI Acquisition Assets.

          “AMI Acquisition Assets” means, with respect to any AMI Acquisition Opportunity, the assets (including, without limitation, the Applicable Assets included within such assets) and equity or other ownership interests subject to such AMI Acquisition Opportunity.

          “AMI Acquisition Opportunity” means the opportunity to acquire either of the following:

          (i) Assets (which includes Applicable Assets) from which 80% or more of the gross revenues derived from such Assets (during the fiscal year ended immediately prior to the

year in which the acquisition in question is to occur) is derived from the following two types of assets combined: (1) natural gas transported on such Applicable Assets that was either received into such Applicable Assets at receipt points located within the AMI Area or delivered from such Applicable Assets at delivery points located within the AMI Area and/or (2) natural gas storage infrastructure assets included in such Applicable Assets; or

          (ii) equity or other ownership interests of an entity which owns Applicable Assets from which 80% or more of the gross revenues derived from such entity’s Assets, on a consolidated basis (during the fiscal year ended immediately prior to the year in which the acquisition in question is to occur) is derived from (1) natural gas transported on such Applicable Assets that was either received into such Applicable Assets at receipt points located within the AMI Area or delivered from such Applicable Assets at delivery points located within the AMI Area and/or (2) natural gas storage infrastructure assets included in such Applicable Assets.

          For the avoidance of doubt, any portion of the “Assets” referred to in clause (i) above and any subsidiary or affiliate of the “entity” referred to in clause (ii) above shall not, on a stand alone basis, constitute an AMI Acquisition Opportunity.

          “AMI Area” means that portion of the area within the State of Louisiana that is designated as the “AMI Area” on Exhibit A hereto.

          “AMI Assets” means all AMI Acquisition Assets and AMI Greenfield Assets.

          “AMI Greenfield Assets” means, with respect to any AMI Greenfield Opportunity, the assets subject to such AMI Greenfield Opportunity.

          “AMI Greenfield Opportunity” means the opportunity to construct and develop (as opposed to an acquisition of) additional Applicable Assets other than any Company Specific Opportunity.

          “AMI Opportunity” means any AMI Acquisition Opportunity or AMI Greenfield Opportunity.

          “Applicable Assets” means interstate and/or intrastate natural gas transportation infrastructure assets (but specifically excluding any Natural Gas Gathering Infrastructure Assets, natural gas treating infrastructure assets and/or natural gas processing infrastructure assets) and natural gas storage infrastructure assets that are located within the AMI Area.

          “Assets” means assets of any type or nature, including, without limitation, Applicable Assets.

          “Available Capacity” means the maximum quantity of natural gas that can be transported in a given period of time under normal operating conditions.

          “Change of Control Event” means any date on which the Ultimate Parent (as defined in the Company Partnership Agreement) of Alinda Investor I Parent and of Alinda Investor II Parent collectively no longer possesses, directly or indirectly, through one or more

intermediaries, (i) more than 25% of the outstanding voting interest in the Company and (ii) more than 25% of the economic or beneficial interest in the Company.

          “Company Specific Opportunity” means any intrastate and/or interstate natural gas transportation infrastructure assets the sole purpose of which are to increase the Available Capacity of the Company’s or RIGS’ existing natural gas transportation infrastructure assets.

          “Management Company” means Regency Employees Management LLC.

          “MC Member” shall have the meaning ascribed to such term in the Company Partnership Agreement.

          “Natural Gas Gathering Infrastructure Assets” means pipelines and other facilities (including all interconnections, laterals, storage facilities, meters, dehydration facilities, compression facilities, junction heaters, separators, electric power lines, communication cables, roads and other related facilities and equipment, including all easements located thereon) used to transport gas from a current production facility to a transmission line or main line.

          “RIGS System” means the gas transportation system consisting of the intrastate pipeline owned by RIGS as of the Closing Date and as thereafter expanded from time-to-time.

          “Services Agreement” means the Master Services Agreement between the Partnership and the Management Company, as amended or modified from time to time, pursuant to which the Management Company manages the day-to-day operations of the Company.

          “Subject Person” means the MLP, any direct or indirect wholly owned subsidiary of the MLP and any Affiliate of the MLP that is directly or indirectly controlled by the MLP; provided, that “Subject Person” shall not include the Company, RIGS or any of their direct or indirect subsidiaries or any Person that directly or indirectly owns any interest in the MLP.

          “Termination Date” means the earlier to occur of (i) the first date on which the MLP and/or its Affiliates, directly or indirectly, owns 75% or more of the GP Units in the Company, (ii) the date on which the Services Agreement is terminated and (iii) the occurrence of a Change of Control Event.

     (b) Term of this Agreement. The term of this Agreement (the “Term”) shall begin on the Closing Date and shall end on the Termination Date. During the Term, the MLP shall, and shall cause each other Subject Person to, comply with all of the provisions of this Agreement and each other Party shall comply with all of the provisions of this Agreement. For the avoidance of doubt, this Agreement shall terminate for all purposes upon the expiration of the Term.

     (c) AMI Acquisition Opportunities.

          (i) In the event that a Subject Person identifies an AMI Acquisition Opportunity that such Subject Person desires to pursue or reasonably believes the Company should pursue, such Subject Person shall promptly notify the Alinda Investors of such opportunity and shall, subject to the Alinda Investors executing and delivering to the Subject Person a confidentiality agreement in form and substance reasonably satisfactory to the Subject

Person, (A) make available to the Alinda Investors all information in its possession related to such AMI Acquisition Opportunity as may be reasonably requested by the Alinda Investors from time to time, including all information concerning and analysis of the business, operations and finances of the applicable AMI Acquisition Assets and the terms of any proposed acquisition agreement, (B) frequently consult with the Alinda Investors in evaluating the AMI Acquisition Opportunity and (C) keep the Alinda Investors reasonably informed as to the status of the AMI Acquisition Opportunity to the extent requested by the Alinda Investors from time-to-time, in each case, subject to any confidentiality restrictions applicable to such Subject Person. Each Subject Person shall use commercially reasonably efforts to cause any confidentiality agreement entered into by such Subject Person in connection with any AMI Acquisition Opportunity to allow disclosures of confidential information to the Alinda Investors.

          (ii) If the Subject Person executes an acquisition agreement for any AMI Acquisition Opportunity, it shall use commercially reasonable efforts to cause the applicable acquisition agreement and all other related agreements and materials (including due diligence materials) (A) to be fully assignable to the Company without the consent of any other Person and (B) to be promptly delivered to the Alinda Investors. The Alinda Investors shall have the lesser of (x) 15 days following the delivery to the Alinda Investors of a complete and accurate copy of the applicable acquisition agreement and all other related agreements in the Subject Person’s possession, or (y) the number of days between the delivery of such agreements and the anticipated closing date thereunder in which to cause the Company to elect to purchase the applicable AMI Acquisition Assets in accordance with the terms of the Company Partnership Agreement (the “AMI Acquisition Election Period”).

          (iii) If the Alinda Investors elect to cause the Company to acquire the AMI Acquisition Opportunity, the Subject Person shall, to the extent permitted by the applicable acquisition agreement and other related agreements, assign its rights thereunder and related materials (including due diligence materials) to the Company, and the Company shall assume all of the Subject Person’s rights and obligations thereunder and (whether or not such agreements can be assigned) agree to protect, defend, indemnify and hold harmless such Subject Person from all liabilities arising out of or related to such acquisition agreement and related agreements. In addition, at the time of such assignment of the applicable acquisition agreement, the Company shall reimburse the Subject Person for all costs and expenses incurred by such Subject Person (and its Affiliates) in connection with such AMI Acquisition Opportunity. If the Alinda Investors elect to cause the Company to acquire the AMI Acquisition Opportunity but the Subject Person is unable to assign the applicable acquisition agreement to the Company, then the Subject Person shall hold the applicable acquisition and related agreements in trust for the benefit of the Company, and, at the time of such election, the Company shall reimburse the Subject Person (and its Affiliates) for all costs and expenses incurred by such Subject Person (and its Affiliates) in connection with such AMI Acquisition Opportunity. In addition, the Subject Person shall use commercially reasonable efforts to cause the AMI Acquisition Assets to be assigned to the Company at the closing or as soon as reasonably practicable thereafter and shall (at the Company’s expense and direction) use commercially reasonable efforts to assign to the Company (or enforce for the benefit of the Company) all of the benefits of the applicable agreements, and, upon such assignment of AMI Acquisition Assets, the Company shall reimburse such Subject Person for any additional costs and expenses incurred by such Subject

Person (and its Affiliates) in connection with the acquisition and assignment of such AMI Acquisition Assets. If the Subject Person is unable to assign the AMI Acquisition Assets at the closing, the Subject Person shall hold such AMI Acquisition Assets in trust for the benefit of Company, and the Company shall reimburse the Subject Person for all costs and expenses incurred by such Subject Person (and its Affiliates) in connection with such AMI Acquisition Assets. Any assignment of the applicable acquisition agreement, related agreements, materials or AMI Acquisition Assets pursuant to this Section 1(c) by a Subject Person to the Company shall be on an “AS IS, WHERE IS” basis, without any representations, warranties, covenants, indemnification or other agreements given by any Subject Person other than that all of the rights of the Subject Person in the assigned agreements or AMI Acquisition Assets is free of all Liens arising by, through or under such Subject Person but not otherwise.

          (iv) With respect to any particular AMI Acquisition Assets, any Subject Person and its Affiliates shall be free to pursue such AMI Acquisition Assets and such AMI Acquisition Assets shall no longer be subject to this Agreement if the Alinda Investors do not elect to cause the Company to acquire the AMI Acquisition Opportunity prior to the expiration of the AMI Acquisition Election Period.

     (d) AMI Greenfield Opportunities.

          (i) In the event a Subject Person identifies an AMI Greenfield Opportunity that such Subject Person desires to pursue or reasonably believes the Company should pursue, such Subject Person shall promptly notify the Company of such opportunity and provide the Company all information in its possession related thereto.

          (ii) The Company shall have the exclusive right to purse the AMI Greenfield Opportunity until such time as there is a good faith, irreconcilable and material disagreement between the Alinda Investors and any Subject Person on the design, revenue or cost structure or risk profile for or other material matter relating to the AMI Greenfield Opportunity (a “Trigger Event”). If a Trigger Event occurs, then any Subject Person and its Affiliates shall be free to pursue such AMI Greenfield Opportunity without the participation by the Company or the Alinda Investors. If, following a Trigger Event, a Subject Person pursues an AMI Greenfield Opportunity outside of the Partnership, then such Subject Person and the Company (without the participation of the MC Member designated by Regency HIG) shall negotiate in good faith to determine the amount of the costs and expenses incurred by the Company with respect to such AMI Greenfield Opportunity to be reimbursed by such Subject Person, if any, and the timing thereof. In the event that, during the continued development of the AMI Greenfield Opportunity the Subject Person modifies the AMI Greenfield Opportunity in such a manner consistent with the position of the Alinda Investors in the dispute between the Alinda Investors and the Subject Person that resulted in the Trigger Event, then such opportunity shall become a new AMI Greenfield Opportunity subject to the provisions in Section 1(d)(i) and this Section 1(d)(ii), and the Alinda Investors shall have 30 days after receipt of notice of such new AMI Greenfield Opportunity to (x) cause the Company to elect to pursue such AMI Greenfield Opportunity, and (y) (if the Alinda Investors cause the Company to so elect) reimburse the Subject Person for all of its costs and expenses associated with such AMI Greenfield Opportunity (equitability adjusted to account for any costs and expenses that would not have been incurred with respect to such AMI Greenfield Opportunity but for the Subject Person’s decision to pursue the AMI Greenfield

Opportunity in a manner inconsistent with the position of the Alinda Investors in the dispute between the Alinda Investors and the Subject Person that resulted in the Trigger Event); provided, that if the Alinda Investors fail to cause the Company to make such election or reimburse the Subject Person for such costs and expenses during such 30 day period, then the Company shall be deemed to have waived any rights under this Agreement to participate in such new AMI Greenfield Opportunity and the Subject Person shall be free to pursue such AMI Greenfield Opportunity without the participation by the Company or the Alinda Investors.

     (e) Scope of Obligation to Offer. The MLP and any other Subject Person shall only be required to offer AMI Acquisition Assets and AMI Greenfield Assets to the Company for purchase or development, as applicable, by the Company upon the terms and conditions contained in this Section 1. Except as provided in this Section 1, each Subject Person shall be free to engage in any business activity whatsoever, including those that may be in direct competition with the Company. For the avoidance of doubt, the Parties hereby acknowledge and agree that the obligations of the Parties set forth in Section 1 shall not apply to any Company Specific Opportunity.

     (f) Non-Compete.

          (i) If and for so long as the Alinda Investors are participating with a Subject Person in the analysis of an identified AMI Acquisition Opportunity pursuant to Section 1(c) and thereafter if the Alinda Investors have caused the Company to acquire the AMI Acquisition Company, then neither of the Alinda Investors shall pursue such AMI Acquisition Opportunity and each of Alinda Investor 1 and Alinda Investor 2 shall cause Alinda Investor I Parent and Alinda Investor II Parent, respectively, to not pursue such AMI Acquisition Opportunity directly or through a Person directly or indirectly wholly owned by Alinda Investor I Parent and Alinda Investor II Parent, respectively, formed solely for the purpose of pursuing and acquiring such AMI Acquisition Opportunity.

          (ii) If the Company is pursuing an AMI Greenfield Opportunity, then until the occurrence of a Trigger Event, neither of the Alinda Investors shall pursue such AMI Greenfield Opportunity and each of Alinda Investor 1 and Alinda Investor 2 shall cause Alinda Investor I Parent and Alinda Investor II Parent, respectively, to not pursue such AMI Greenfield Opportunity directly or through a Person directly or indirectly wholly owned by Alinda Investor I Parent and Alinda Investor II Parent, respectively, formed solely for the purpose of pursuing and acquiring such AMI Greenfield Opportunity.

     Section 2. Confidentiality. Each Party covenants and agrees that all information submitted to it by any Subject Person under this Agreement will be considered proprietary, confidential and the property of the Subject Person and will be used only for the purpose of determining whether or not to exercise its rights in Section 1 and, if such election is exercised, for use in the development and operation of the applicable AMI Opportunity; provided, however such information shall become the property of the Company at such time that the Company elects to pursue an AMI Opportunity as provided in Section 1; provided, further, if a Trigger Event occurs with respect to any AMI Greenfield Opportunity, any applicable information shall revert back to the applicable Subject Person.

     Section 3. Binding Effect. This Agreement will be binding upon, and will inure to the benefit of, the Parties and their respective successors, permitted assigns and legal representatives and each of the Partners shall cause the obligations under this Agreement to be assumed by any its successors or assigns of any interest in the Company.

     Section 4. No Third Party Rights. The provisions of this Agreement are intended to bind the Parties as to each other and are not intended to and do not create rights in any other person or confer upon any other person any benefits, rights or remedies and no person is or is intended to be a third party beneficiary of any of the provisions of this Agreement.

     Section 5. No Waiver. No waiver or consent, express or implied, by any Party to or of any breach or default by any person in the performance by such person of its obligations hereunder shall be deemed or construed to be a consent or waiver to or of any other breach or default in the performance by such person of the same or any other obligations of such person hereunder. Failure on the part of a Party to complain of any act of any person or to declare any person in default, irrespective of how long such failure continues, shall not constitute a waiver by such Party of its rights hereunder until the applicable statute of limitations period has run.

     Section 6. Applicable Law. THIS AGREEMENT IS GOVERNED BY AND SHALL BE CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF DELAWARE, EXCLUDING ANY CONFLICT-OF-LAWS RULE OR PRINCIPLE THAT MIGHT REFER THE GOVERNANCE OR THE CONSTRUCTION OF THIS AGREEMENT TO THE LAW OF ANOTHER JURISDICTION. A PARTY MAY BRING AN ACTION ARISING UNDER OR RELATING TO THIS AGREEMENT, IF AT ALL, ONLY IN A FEDERAL OR STATE COURT OF COMPETENT JURISDICTION IN WILMINGTON, DELAWARE. EACH PARTY HEREBY IRREVOCABLY WAIVES ANY OBJECTION, INCLUDING, WITHOUT LIMITATION, ANY OBJECTION TO THE LAYING OF VENUE OR BASED ON THE GROUNDS OF FORUM NON-CONVENIENCE, WHICH IT MAY NOW OR HEREAFTER HAVE TO THE BRINGING OF SUCH ACTION OR PROCEEDING IN ANY SUCH RESPECTIVE JURISDICTION.

     Section 7. Severability. If any of the provisions of this Agreement are held by any court of competent jurisdiction to contravene, or to be invalid under, the laws of any political body having jurisdiction over the subject matter hereof, such contravention or invalidity shall not invalidate the entire Agreement. Instead, this Agreement shall be construed as if it did not contain the particular provision or provisions held to be invalid and an equitable adjustment shall be made and necessary provision added so as to give effect to the intention of the Parties as expressed in this Agreement at the time of execution of this Agreement.

     Section 8. Amendment or Modification. This Agreement may be amended, modified or supplemented from time to time only by a written agreement executed by all Parties other than the Company.

     Section 9. Assignment. No Party shall have the right to assign its rights or obligations under this Agreement without the prior written consent of the other Parties; provided, that any Alinda Investor may assign its rights and obligations under this Agreement to any Affiliate of such Alinda Investor that is a permitted transferee of such Alinda Investor’s GP

Units (as defined in the Company Partnership Agreement) in accordance with the terms of the Company Partnership Agreement but no such permitted assignment shall be deemed to be a limitation on Section 1(b).

     Section 10. Counterparts. This Agreement may be executed in any number of counterparts with the same effect as if all Parties had signed the same document. All counterparts shall be construed together and shall constitute one and the same instrument. Execution and delivery of this Agreement by exchange of facsimile or other electronically transmitted counterparts bearing the signature of a Party shall be equally as effective as delivery of a manually executed counterpart by such Party.

     Section 11. No Recourse. For the avoidance of doubt, except as expressly provided herein, the provisions of this Agreement shall not give rise to any right of recourse against any directors, members, managers, stockholders, owners, officers, partners, employees, agents, consultants, attorneys or representatives of any Party.

     Section 12. Entire Agreement; Supersedure. This Agreement and the instruments referenced herein and therein supersede all previous understandings or agreements among the Parties, whether oral or written, with respect to their subject matter. This Agreement and such instruments contain the entire understanding of the Parties with respect to the subject matter hereof and thereof. No understanding, representation, promise or agreement, whether oral or written, is intended to be or shall be included in or form part of this Agreement unless it is contained in a written amendment hereto executed by the Parties after the date hereof except as provided in Section 8.

     Section 13. No Partnership, Agency, Etc. The relationship created hereby between the Parties is contractual. Nothing herein shall be deemed to create a partnership, agency, independent contractor or other relationship between the parties for any purpose.

[Signature Page Follows]

     IN WITNESS WHEREOF, this Agreement has been duly executed by the Parties as of the date first above written.

Signature Page to AMI Agreement

EXHIBIT A

AMI AREA